A symmetric splitting method for rigid body dynamics

• Published in: Modeling, identification and control Vol. 27; no. 2; pp. 95 - 108
• Main Authors: Celledoni, E., Säfström, N.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Oslo Research Council of Norway 01.04.2006; Norsk Forening for Automatisering (NFA); Norwegian Society of Automatic Control
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Rigid bodies; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics; symmetric methods; symplectic methods; Rigid bodies; Euler equation; Equation of motion; Jacobi elliptic functions; Decomposition method; Solid dynamic; Elliptic function; symplectic methods; Modeling; Geometric mean; Arithmetic mean; symmetric methods; Vector field; Symplectic manifold
• ISSN: 0332-7353; 1890-1328
• DOI: 10.4173/mic.2006.2.2

It has been known since the time of Jacobi that the solution to the free rigid body (FRB) equations of motion is given in terms of a certain type of elliptic functions. Using the Arithmetic-Geometric mean algorithm, (1), these functions can be calculated efficiently and accurately. The overall approach yields a faster and more accurate numerical solution to the FRB equations compared to standard numerical ODE and symplectic solvers. In this paper we investigate the possibility of extending this approach to the case of rigid bodies subject to external forces. By using a splitting strategy similar to the one proposed in (14), we decompose the vector field of our problem in a FRB problem and another completely integrable vector field. We apply the method to the simulation of the heavy top.